a. g. aksoy j. antoine m. a. khamsi complex time-delay ... › sgw › documents › 815837 ›...

springer.com/booksellers 29Springer News 11/12/2009 Mathematics

A. G. Aksoy, Claremont McKenna College, Claremont, CA, USA; M. A. Khamsi, University of Texas at El Paso, El Paso, TX, USA

A Problem Book in Real Analysis

Today, nearly every undergraduate mathematics program requires at least one semester of real analysis. Often, students consider this course to be the most challenging or even intimidating of all their mathematics major requirements. The primary goal of A Problem Book in Real Analysis is to alleviate those concerns by systematically solving the problems related to the core concepts of most analysis courses. In doing so, the authors hope that learning analysis becomes less taxing and more satisfying. The wide variety of exercises presented in this book range from the computational to the more conceptual and varies in difficulty. They cover the following subjects: set theory; real numbers; sequences; limits of the functions; continuity; differentiability; integration; series; metric spaces; sequences; and series of functions and fundamen-tals of topology. Furthermore, the authors define the concepts and cite the theorems used at the beginning of each chapter.

Features7 Helps instructors enhance lectures with problems beyond the classroom 7 Helps prepare students for examinations 7 Text encourages students to find different solutions to problems than those presented

ContentsPreface.- Elementary Logic and Set Theory.- Real Numbers.- Sequences.- Limits of Func-tions.- Continuity.- Differentiability.- Integra-tion.- Series.- Metric Spaces.- Fundamentals of Topology.- Sequences and Series of Functions.- Index.- References.

Fields of interestAnalysis

Target groupsUndergraduate students

J. Antoine, Université catholique de Louvain, Louvain-la-Neuve, Belgium; C. Trapani, Università di Palermo, Italy

Partial Inner Product SpacesTheory and Applications

Partial Inner Product (PIP) Spaces are ubiquitous, e.g. Rigged Hilbert spaces, chains of Hilbert or Banach spaces (such as the Lebesgue spaces Lp over the real line), etc. In fact, most functional spaces used in (quantum) physics and in signal processing are of this type. The book contains a systematic analysis of PIP spaces and opera-tors defined on them. Numerous examples are described in detail and a large bibliography is provided. Finally, the last chapters cover the many applications of PIP spaces in physics and in signal/image processing, respectively. As such, the book will be useful both for researchers in mathematics and practitioners of these disciplines.

Contents1 General Theory : Algebraic Point of View.- 2 General Theory : Topological Aspects.- 3 Opera-tors on PIP-spaces and Indexed PIP-spaces.- 4 Examples of Indexed PIP-spaces.- 5 Refinements of PIP-spaces.- 6 Partial *-algebras of Operators in a PIP-space.- 7 Applications in Mathematical Physics.- 8 PIP-spaces and Signal Processing.

Fields of interestFunctional Analysis; Operator Theory; Quantum Field Theories, String Theory

Target groupsResearchers and graduate students in mathematics, physics and signal and image processing

F. Atay, MPI Leipzig, Germany (Ed.)

Complex Time-Delay SystemsTheory and Applications

Time delays in dynamical systems arise as an inevitable consequence of finite speeds of infor-mation transmission. Realistic models increas-ingly demand the inclusion of delays in order to properly understand, analyze, design, and control real-life systems. The goal of this book is to present the state-of-the-art in research on time-delay dynamics in the framework of complex systems. While the theory of delay equations is quite mature, its application to the particular problems of complex systems and complexity is a newly emerging field, and the present volume aims to play a pioneering role in this perspective. The chapters in this volume are authored by renowned experts and cover both theory and applications in a wide range of fields, with examples from neurosciences, traffic dynamics and laser physics. Furthermore, all chapters include sufficient introductory material and extensive bibliographies, making the book a self-contained reference for both graduate students and active researchers alike.

From the contentsFinite Propagation Speeds in Spatially Extended Systems.- Global Convergent Dynamics of Delayed Neural Networks.- Amplitude Death, Synchrony, and Chimera States in Delay Coupled Limit Cycle Oscillators.- Stochastic Delay-Differential Equa-tions.- Time-Delayed Feedback Control: From Simple Models to Lasers and Neural Systems.- Deterministic Time-Delayed Traffic Flow Models: A Survey.

Fields of interestSystems Theory, Control; Statistical Physics, Dynamical Systems and Complexity; Mathematical Biology in General

Target groupsPostgraduate students and researchers in natural and physical sciences, engineering and applied mathematics

Type of publicationGraduate/Advanced undergraduate textbook

Mathematics

Due November 2009

2010. X, 254 p. 17 illus., 8 in color. (Problem Books in Mathematics) Hardcover

7 € 49,95 | £44.997 * € (D) 53,45 | € (A) 54,95 | sFr 77,50ISBN 978-1-4419-1295-4

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Type of publicationMonograph

Mathematics

Due November 2009

2009. XII, 332 p. (Lecture Notes in Mathematics, Volume 1986) Softcover

7 € 69,95 | £62.997 * € (D) 74,85 | € (A) 76,95 | sFr 109,00ISBN 978-3-642-05135-7

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Mathematics

Due February 2010

2010. Approx. 320 p. (Understanding Complex Systems) Hardcover

7 € 89,95 | £81.007 * € (D) 96,25 | € (A) 98,95 | sFr 140,00ISBN 978-3-642-02328-6

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www.springer.com/978-1-4419-1295-4



springer.com/booksellers30 Springer News 11/12/2009Mathematics

Y. Azmy, Pennsylvania State University, University Park, PA, USA; E. Sartori, OECD, Issy-les-Moulineaux, France

Nuclear Computational ScienceA Century in Review

Nuclear engineering has undergone extensive progress over the years. In the past century, colossal developments have been made and with specific reference to the mathematical theory and computational science underlying this discipline, advances in areas such as high-order discretization methods, Krylov Methods and Iteration Accelera-tion have steadily grown. Nuclear Computational Science: A Century in Review addresses these topics and many more; topics which hold special ties to the first half of the century, and topics focused around the unique combination of nuclear engineering, computational science and mathematical theory. Comprising eight chapters, Nuclear Computa-tional Science: A Century in Review incorporates a number of carefully selected issues representing a variety of problems, providing the reader with a wealth of information in both a clear and concise manner. The comprehensive nature of the coverage and the stature of the contributing authors combine to make this a unique landmark publication. Targeting the medium to advanced level academic, this book will appeal to researchers and students with an interest in the progression of mathematical theory and its application to nuclear computa-tional science.

Fields of interestNuclear Engineering; Applications of Mathematics; Theoretical, Mathematical and Computational Physics

Target groupsAdvanced level academic, researchers and students

J. C. Baez, J. P. May (Eds.)

Towards Higher Categories

The purpose of this book is to give background for those who would like to delve into some higher category theory. It is not a primer on higher category theory itself. It begins with a paper by John Baez and Michael Shulman which explores informally, by analogy and direct connection, how cohomology and other tools of algebraic topology are seen through the eyes of n-category theory. The idea is to give some of the motivations behind this subject. There are then two survey articles, by Julie Bergner and Simona Paoli, about (infinity,1) categories and about the algebraic modelling of homotopy n-types. These are areas that are particularly well understood, and where a fully integrated theory exists. The main focus of the book is on the richness to be found in the theory of bicategories, which gives the essential starting point towards the understanding of higher cate-gorical structures. An article by Stephen Lack gives a thorough, but informal, guide to this theory. A paper by Larry Breen on the theory of gerbes shows how such categorical structures appear in differential geometry.

Features7 Thorough but informal guide to the theory of higher categorical structures

ContentsForeword.- Preface.- Lectures on n-categories and cohomology.- A survey of (1, 1)-categories.- Internal categorical structures in homotopical algebra.- A 2-categories companion.- Notes on 1- and 2-gerbes.- An Australian conspectus of higher categories.- IMA summer program participants.

Fields of interestCategory Theory, Homological Algebra; Algebraic Topology; Topology

Target groupsResearchers, graduate students

J. Barnes, Caversham, Reading, UK

Gems of Geometry

Based on a series of lectures for adult students, this lively and entertaining book proves that, far from being a dusty, dull subject, geometry is in fact full of beauty and fascination. The author’s infectious enthusiasm is put to use in explaining many of the key concepts in the field, starting with the Golden Number and taking the reader on a geometrical journey via Shapes and Solids, through the Fourth Dimension, finishing up with Einstein’s Theories of Relativity. Aimed at a general readership, the text makes accessible complex subjects such as Chaos and Fractals. It includes a wealth of the author’s own illustrations and features appendices on related topics. Equally suitable as a gift for a youngster or as a nostalgic journey back into the world of math-ematics for older readers, John Barnes’ book is the perfect antidote for anyone whose maths lessons at school are a source of painful memories. Where once geometry was a source of confusion and frustration, Barnes brings enlightenment and entertainment.

Features7 Enjoyable book on geometry, understandable by everybody

Contents1 The Golden Number.- 2 Shapes and Solids.- 3 The Forth Dimension.- 4 Projective Geometry.- 5 Topology.- 6 Bubbles.- 7 Harmony of the Spheres.- 8 Chaos and Fractals.- 9 Relativity.- 10 Finale.- A More on Four.- B Crystals.- C Stability.- D Stereo Images.- E Schlegel Images.- F Stability.- G Fanoland.- Bibliography.- Index.

Field of interestGeometry

Target groupsGeneral readers with an interest in mathematics and scienceType of publication

Contributed volume

Engineering

Due December 2009

2010. IX, 493 p. 48 illus., 1 in color. Hardcover

7 approx. € 109,95 | £79.997 approx. * € (D) 117,65 | € (A) 120,95 | sFr 171,00ISBN 978-90-481-3410-6

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Mathematics

Due November 2009

2010. XIII, 283 p. (The IMA Volumes in Mathematics and its Applications, Volume 152) Hardcover

7 € 89,95 | £81.007 * € (D) 96,25 | € (A) 98,95 | sFr 140,00ISBN 978-1-4419-1523-8

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Type of publicationPopular science

Mathematics

Due December 2009

2010. XII, 336 p. Hardcover


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R. I. Bot, Chemnitz University of Technology, Germany

Conjugate Duality in Convex Optimization

This book presents new achievements and results in the theory of conjugate duality for convex optimization problems. The perturbation approach for attaching a dual problem to a primal one makes the object of a preliminary chapter, where also an overview of the classical generalized interior point regularity conditions is given. A central role in the book is played by the formulation of generalized Moreau-Rockafellar formulae and closedness-type conditions, the latter constituing a new class of regularity conditions, in many situations with a wider applicability than the generalized interior point ones. The reader also receives deep insights into biconjugate calculus for convex functions, the relations between different existing strong duality notions, but also into several unconventional Fenchel duality topics. The final part of the book is consecrated to the applications of the convex duality theory in the field of monotone operators.

ContentsIntroduction.- Pertubation Functions and Dual Problems.- Moreau-Rockafellar Formulae and Closedness-Type Regularity Conditions.- Bicon-jugate Functions.- Strong and Total Conjugate Duality.- Unconventional Fenchel Duality.- Appli-cations of the Duality to Monotone Operators.

Fields of interestOperations Research, Mathematical Programming; Operations Research/Decision Theory; Optimiza-tion

Target groupsScientists

J. Brasselet, IML-CNRS, Marseille, France; J. Seade, UNAM, Cuernavaca, México; T. Suwa, Hokkaido University, Sapporo, Japan

Vector fields on Singular Varieties

Vector fields on manifolds play a major role in mathematics and other sciences. In particular, the Poincaré-Hopf index theorem gives rise to the theory of Chern classes, key manifold-invariants in geometry and topology. It is natural to ask what is the ‘good’ notion of the index of a vector field, and of Chern classes, if the underlying space becomes singular. The question has been explored by several authors resulting in various answers, starting with the pioneering work of M.-H. Schwartz and R. MacPherson. We present these notions in the framework of the obstruction theory and the Chern-Weil theory. The interplay between these two methods is one of the main features of the monograph.

Fields of interestSeveral Complex Variables and Analytic Spaces; Dynamical Systems and Ergodic Theory; Mani-folds and Cell Complexes (incl. Diff.Topology)

Target groupsResearchers and graduate students in algebraic geometry, complex analytic geometry, algebraic topology, and differential geometry

H. Brézis, Rutgers University, Piscataway, NJ, USA

Functional Analysis, Sobolev Spaces and Partial Differential Equations

This textbook is a completely revised, updated, and expanded English edition of the important Analyse fonctionnelle (1983). In addition, it contains a wealth of problems and exercises (with solutions) to guide the reader. Uniquely, this book presents in a coherent, concise and unified way the main results from functional analysis together with the main results from the theory of partial differential equations (PDEs). Although there are many books on functional analysis and many on PDEs, this is the first to cover both of these closely connected topics. Since the French book was first published, it has been translated into Spanish, Italian, Japa-nese, Korean, Romanian, Greek and Chinese. The English edition makes a welcome addition to this list.

Features7 Major textbook by a well-known and highly regarded author 7 Only single-volume textbook to cover related fields of functional analysis and PDEs

From the contents1. The Hahn–Banach Theorems. Introduction to the Theory of Conjugate Convex Functions.- 2. The Uniform Boundedness Principle and the Closed Graph Theorem. Unbounded Operators. Adjoint. Characterization of Surjective Operators.- 3. Weak Topologies. Reflexive Spaces. Separable Spaces. Uniform Convexity.- 4. L^p Spaces.- 5. Hilbert Spaces.- 6. Compact Operators. Spectral Decom-position of Self-Adjoint Compact Operators.- 7. The Hille–Yosida Theorem.- 8. Sobolev Spaces and the Variational Formulation of Boundary Value Problems in One Dimension.

Fields of interestFunctional Analysis; Partial Differential Equations

Target groupsUndergraduate and graduate students in math-ematics and related fields including physics, engineering and finance


Mathematics

Due January 2010

2010. Approx. 160 p. (Lecture Notes in Economics and Mathematical Systems, Volume 637) Softcover

7 € 69,95 | £62.997 * € (D) 74,85 | € (A) 76,95 | sFr 109,00ISBN 978-3-642-04899-9

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Mathematics

Due December 2009

2009. Approx. 250 p. (Lecture Notes in Mathematics, Volume 1987) Softcover

7 € 44,95 | £40.997 * € (D) 48,10 | € (A) 49,45 | sFr 70,00ISBN 978-3-642-05204-0

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Mathematics

Due February 2010

2010. Approx. 455 p. (Universitext) Softcover


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R. W. Bruggeman, University of Utrecht, The Netherlands

Families of Automorphic Forms

This book gives a systematic treatment of real analytic automorphic forms on the upper half plane for general confinite discrete subgroups. These automorphic forms are allowed to have exponential growth at the cusps and singulari-ties at other points as well. It is shown that the Poincaré series and Eisenstein series occur in families of automorphic forms of this general type. These families are meromorphic in the spectral parameter and the multiplier system jointly. The general part of the book closes with a study of the singularities of these families. The work is aimed primarily at mathematicians working on real analytic automorphic forms. However, the book will also encourage readers at the graduate level (already versed in the subject and in spectral theory of automorphic forms) to delve into the field more deeply.

From the reviews7 This book is an indispensable tool for anyone working in Boolean algebra, and is also recom-mended for set-theoretic topologists 7 Zentralblatt MATH

Features7 New material so far mostly available in artcicles only

Field of interestReal Functions

Target groupsMathematicians, graduates

L. Bruna, J. Girbau, Universitat Autònoma de Barcelona, Spain

Stability by Linearization of Einstein’s Field Equation

The aim of this book is to establish the precise mathematical framework in which linearization stability of Einstein equation with matter makes sense, and once this is achieved, to find conditions for this type of stability when a Robertson-Walker model for the universe is considered. The concept of linearization stability arises when one wonders whether the solutions of a linearized equation do really approximate solutions of the corresponding true equation. This requires a new definition of linearization stability adapted to Einstein equation, a bit different from the classical one. However, this new definition can not be applied directly to the Einstein equation because energy conditions ties both deformations of the metric and of the stress-energy tensor. Therefore, one must look for a background where the variables representing the geometry and the energy-matter are indepen-dent. This representation is given by a well-posed Cauchy problem for the Einstein’s field equations.

Features7 Contains classical results on stability of great beauty which should be far better known than they are, both by mathematicians and by physicists 7 Self-contained book where all the objects needed to prove the theorems are presented in a motivated way 7 Provides introductory chapters on pseudo-Riemannian manifolds and relativity (both special and general) addressed to readers having no background in these topics

Fields of interestTheoretical, Mathematical and Computational Physics

Target groupsGraduate (or advanced undergraduate) students, researchers in mathematics and physics

G. Cesari, J. Aquilina, N. Charpillon, Z. Filipovic, G. Lee, I. Manda, UBS London, United Kingdom

Modelling, Pricing, and Hedging Counterparty Credit ExposureA Technical Guide

The credit crisis that started in 2007, with the collapse of well-established financial institutions and the bankruptcy of many public corporations, has clearly shown the importance for any company entering the derivative business of modelling, pricing, and hedging its counterparty credit exposure. Building an accurate representation of firm-wide credit exposure, for both risk and trading activi-ties, is a significant challenge from the technical as well as the practical point of view. This volume can be considered as a roadmap to finding practical solutions to the problem of computing counterparty credit exposure for large books of both vanilla and exotic derivatives usually traded by large Investment Banks. It is divided into four parts, (I) Methodology, (II) Architecture and Implementation, (III) Products, and (IV) Hedging and Managing Counterparty Risk.

From the contentsPart I: Methodology.- 1.Introduction.- 2.Modelling Framework.- 3.Simulation Models.- 4.Valuation and Sensitivities.- Part II: Architecture and Implementation.- 5.Computational Frame-work.- 6.Implementation.- 7.Architecture.- Part III: Products.- 8.Interest Rate Products.- 9.Equity, Commodity, Inflation and FX Products.- 10.Credit Derivatives.

Fields of interestQuantitative Finance; Probability Theory and Stochastic Processes; Statistics for Business/Economics/Mathematical Finance/Insurance

Target groupsMathematicians and reseachers interested in finance: credit exposure computation, credit valu-ation adjustment, pricing derivative mathematics, application to finance, stochastic calculus, busi-ness, credit risk


Mathematics

Due November 2009

Originally published in the series: Monographs in Mathematics Vol 88

1st ed. 1994. 2nd printing 2010. Approx. 330 p. (Modern Birkhäuser Classics) Softcover

7 € 34,95 | £31.997 * € (D) 37,40 | € (A) 38,45 | sFr 59,90ISBN 978-3-0346-0335-5

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Physics and Astronomy

Due April 2010

2010. Approx. 225 p. (Progress in Mathematical Physics, Volume 60) Hardcover

7 € 59,95 | £53.997 * € (D) 64,15 | € (A) 65,95 | sFr 99,00ISBN 978-3-0346-0303-4

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Mathematics

Due November 2009

2010. X, 226 p. (Springer Finance) Hardcover


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W. A. Chaovalitwongse, Rutgers University, Pisca-taway, NJ, USA; P. M. Pardalos, P. Xanthopoulos, University of Florida, Gainesville, FL, USA (Eds.)

Computational Neuroscience

The human brain is among the most complex systems known to mankind. Neuroscientists seek to understand brain function through detailed analysis of neuronal excitability and synaptic transmission. Only in the last few years has it become feasible to capture simultaneous responses from large enough numbers of neurons to empiri-cally test the theories of human brain function. This book will contain the state of art research papers on the field of computational neuroscience. This volume bridges a vital gap between the mathematical sciences and neuroscience research by bringing research areas from scientific and medical fields together. The volume will cover a wide range of research topics with a common goal of better understanding the human neurophysi-ological systems. The contributors are chosen from those who have closely been involved in many diverse applications in neuroscience field. Authors from many disiplines (Electrical Engineering, Biomedical Engineering, Industrial Engineering, medicine) present their latest research results. Data mining, signal processing, optimization and medical science are combined to tackle the most challenging modern neuroscience problems.

Features7 Presents major results and latest trends in the field of computational neuroscience 7 Provides a collection of selected contributions giving a state-of-the-art account of recent developments in the field 7 Includes chapters written by experts in their respective disciplines

Fields of interestComputational Mathematics and Numerical Analysis; Neurosciences; Biomedical Engineering

Target groupsScientists, doctors, graduate students, and prac-titioners in engineering (electrical, industrial, biomedical), applied mathematics, and medical science

E. Cole, University of Leeds, UK

Mathematical and Numerical Modelling of Heterostructure Semiconductor Devices: From Theory to Programming

The commercial development of novel semicon-ductor devices requires that their properties be examined as thoroughly and rapidly as possible. These properties are investigated by obtaining numerical solutions of the highly nonlinear coupled set of equations which govern their behaviour. This book presents some of the mathematical and numerical techniques associated with the inves-tigation. It begins with introductions to quantum and statistical mechanics. Later chapters then cover finite differences; multigrids; upwinding techniques; simulated annealing; mesh generation; and the reading of computer code in C++. The author explains how the methods can be adapted to the specific needs of device modelling, the advantages and disadvantages of each method, the pitfalls to avoid, and practical hints and tips for successful implementation. Sections of computer code are included to illustrate the methods used.

Features7 Entirely self-contained: the basic ideas of quantum mechanics and statistical mechanices are introduced and developed and numerical tech-niques, such as multigrids and genetic computing, are explained in a manner that is comprehensible to readers who have had no previous contact with these subjects

Fields of interestMathematical Modeling and Industrial Math-ematics; Appl. Mathematics/Computational Methods of Engineering; Mathematical Methods in Physics

Target groupsLecturers and researchers working in the fields of electronic engineering and physics, advanced undergraduate and graduate students in electronic engineering and physics, advanced undergraduate and graduate students in mathematics who wish to become involved in numerical modeling

C. Constanda, University of Tulsa, OK, USA

Dude, Can You Count? Stories, Challenges and Adventures in Mathematics

Loosely speaking, Dude, Can You Count? is Algebra Class meets The Hitchhiker’s Guide to the Galaxy. Its unusual central character, JJ, who claims to have a unique vantage position from which he can measure and monitor humanity’s progress, offers a satirical evaluation of the public’s attitude to numeracy and logic, highlighting a few questionable aspects of society and its institutions. The book is an exciting blend of animated conver-sation, fact, humor, wit, light scholarly argument, and elementary challenges, all fused together by a free-flowing and entertaining narrative. Could JJ be right in his assessment of our future prospects? His last act is a call to the readers to make up their own minds and reflect on the importance of what is arguably the most powerful weapon against ignorance: a sound mathematical education. This quirky volume may not solve the major problems facing us today, but should inspire anyone with an inquisitive mind and an interest in learning to think about them.

From the contents1. JJ and the MICQ.- 2. The Mathematical Commandments.- 3. The Public School System.- 4. The School Mathematical Education.- 5. Language, Grammar, and Punctuation.- 6. Foreign Languages.- 7. Foreign Countries and Foreigners.- 8. Mathematics and the Public.- 9. The Question of Calculus.- 10. Political Correctness.- 11. TV Advertising.- 12. Highway Driving.- 13. Units of Measurement.- 14. Percentages and Living on Debt.- 15. Modern Art.- 16. Averages and Buying Cars.- 17. The Public Media.- 18. The Criminal Legal System.- 19. Civil Litigation.

Fields of interestMathematics, general; Popular Science in Math-ematics/Computer Science/Natural Science/Tech-nology; Algebra

Target groupsGeneral readers with an interest in mathematics/popular science

Type of publicationContributed volume

Mathematics

Due March 2010

2010. Approx. 415 p. 78 illus. (Springer Optimization and Its Applications, Volume 39) Hardcover


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Mathematics

Due December 2009

2010. Approx. 420 p. 40 illus. Softcover

7 € 59,95 | £39.957 * € (D) 64,15 | € (A) 65,95 | sFr 93,50ISBN 978-1-84882-936-7

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Type of publicationPopular science

Mathematics

Due December 2009

2010. Approx. 310 p. 25 illus. Dustjacket

7 € 27,95 | £19.997 * € (D) 29,91 | € (A) 30,75 | sFr 43,50ISBN 978-1-84882-538-3

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M. M. Deza, M. Laurent, Laboratoire d’Informatique de l’Ecole Normale Superieure, Paris, France

Geometry of Cuts and Metrics

Cuts and metrics are well-known objects that arise - independently, but with many deep and fascinating connections - in diverse fields: in graph theory, combinatorial optimization, geometry of numbers, combinatorial matrix theory, statistical physics, VLSI design etc. This book presents a wealth of results, from different mathematical disciplines, in a unified comprehensive manner, and establishes new and old links, which cannot be found elsewhere. It provides a unique and invaluable source for researchers and graduate students.

From the reviews7 This book is definitely a milestone in the litera-ture of integer programming and combinatorial optimization. It draws from the Interdisciplinarity of these fields […]. With knowledge about the relevant terms, one can enjoy special subsections without being entirely familiar with the rest of the chapter. This makes it not only an interesting research book but even a dictionary. […] The longer one works with it, the more beautiful it becomes 7 Optima 56, 1997.

ContentsI. Outline of the Book.- 2. Basic Definitions.- Part I Measure Aspects: l1-Embeddability and Probability.- Part II Hypermetric Spaces: an Approach via Geometry of Numbers.- Part III Isometric Embeddings of Graphs.- Part IV Hyper-cube Embeddings and Designs.- Part V Facets of the Cut Cone and Polytope.- Bibliography.- Notation Index.- Subject Index.

Fields of interestCombinatorics; Convex and Discrete Geometry; Number Theory

Target groupsResearchers and graduate students working in the field of discrete mathematics

V. Dragan, T. Morozan, Institute of Mathematics of the Romanian Academy, Bucharest, Romania; A. Stoica, University “Politechnica” of Bucharest, Bucharest, Romania

Mathematical Methods in Robust Control of Discrete-Time Linear Stochastic Systems

In this monograph the authors develop a theory for the robust control of discrete-time stochastic systems, subjected to both independent random perturbations and to Markov chains. Such systems are widely used to provide mathematical models for real processes in fields such as aerospace engineering, communications, manufacturing, finance and economy. The theory is a continuation of the authors’ work presented in their previous book entitled “Mathematical Methods in Robust Control of Linear Stochastic Systems” published by Springer in 2006.

Features7 Provides a common unifying framework for discrete-time stochastic systems corrupted with both independent random perturbations and with Markovian jumps which are usually treated separately in the control literature 7 Covers preliminary material on probability theory, inde-pendent random variables, conditional expectation and Markov chains 7 Proposes new numerical algorithms to solve coupled matrix algebraic Riccati equations 7 Leads the reader in a natural way to the original results through a systematic presentation

Fields of interestSystems Theory, Control; Optimization; Numerical Analysis

Target groupsGraduate students, researchers in advanced control engineering, mathematical systems theory and financec, numerical analysis

K. L. Duggal, University of Windsor, ON, Canada; B. Sahin, Inonu University, Turkey

Differential Geometry of Lightlike Submanifolds

This book presents a comprehensive up-to-date research on the latest developments in differential geometry of lightlike (degenerate) subspaces. The main focus is on hypersurfaces and a variety of submanifolds of indefinite Kählerian, Sasakian and quaternion Kähler manifolds. The primary objects of study are non-degenerate screen distributions, Cauchy-Rieman (CR) structures and their inter-related induced vector bundles. The book also contains several latest physical applications, ample solved examples and the subject matter is designed for a wider audience.

Features7 There does not exist any other book covering the material presented in this volume. This makes the book a uniquely comprehensive work in the field 7 Ffirst book which contains unique exis-tence theorems (with proofs) for the screen distri-butions of lightlike submanifolds 7 Applications are focused on time-dependent realistic models of black hole horizons, lightlike versions of Osserman geometry, harmonic maps and morphisms, CR and contact structures in physics

From the contents1 Preliminaries.- 2 Lightlike hypersurfaces.- 3 Applications of lightlike hypersurfaces.- 4 Half-lightlike submanifolds.- 5 Lightlike submanifolds.- 6 Submanifolds of indefinite Kähler manifolds.- 7 Submanifolds of indefinite Sasakian manifolds.- 8 Submanifolds of Indefinite quaternion Kähler manifolds.- 9 Applications of lightlike geometry.

Fields of interestDifferential Geometry

Target groupsGraduate students, research associates and faculty working in differential geometry and mathematical physics


Mathematics

Due November 2009Previously announced in Springer News 10/2009

1st ed. 1997. 2nd printing 2010. XII, 587 p. 94 illus. (Algorithms and Combinatorics, Volume 15) Softcover

7 € 99,95 | £90.007 * € (D) 106,95 | € (A) 109,95 | sFr 155,50ISBN 978-3-642-04294-2

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Mathematics

Due March 2010

2010. Approx. 310 p. 3 illus. Hardcover


9<HTMEPB=jagcji>


Mathematics

Due March 2010

2010. Approx. 500 p. (Frontiers in Mathematics) Softcover

7 € 59,95 | £53.997 * € (D) 64,15 | € (A) 65,95 | sFr 99,00ISBN 978-3-0346-0250-1

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J. Elias, J. Giral, R. M. Miró-Roig, S. Zarzuela, Universitat de Barcelona, Spain (Eds.)

Six Lectures on Commutative Algebra

Interest in commutative algebra has surged over the past decades. In order to survey and highlight recent developments in this rapidly expanding field, the Centre de Recerca Matematica in Bellaterra organized a ten-days Summer School on Commutative Algebra in 1996. Lectures were presented by six high-level specialists, L. Avramov (Purdue), M.K. Green (UCLA), C. Huneke (Purdue), P. Schenzel (Halle), G. Valla (Genova) and W.V. Vasconcelos (Rutgers), providing a fresh and extensive account of the results, techniques and problems of some of the most active areas of research. The present volume is a synthesis of the lectures given by these authors. Research workers as well as graduate students in commutative algebra and nearby areas will find a useful over-view of the field and recent developments in it.

From the reviews7 All six articles are at a very high level; they provide a thorough survey of results and methods in their subject areas, illustrated with algebraic or geometric examples 7 Acta Sci. Math.

Features7 Synthesis of lectures in a Summer School given at the Centre de Recerca Matematica in Bellaterra (Spain) 7 Fresh and extensive account of the results, techniques and problems of some of the most active areas of research

Fields of interestAlgebra

Target groupsGraduates, postgraduates and researchers in commutative and homological algebra

K. Feng, M. Qin, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing, China

Symplectic Geometric Algorithms for Hamiltonian Systems

“Symplectic Geometric Algorithms for Hamilto-nian Systems” will be useful not only for numerical analysts, but also for those in theoretical physics, computational chemistry, celestial mechanics, etc. The book generalizes and develops the generating function and Hamilton-Jacobi equation theory from the perspective of the symplectic geom-etry and symplectic algebra. It will be a useful resource for engineers and scientists in the fields of quantum theory, astrophysics, atomic and molec-ular dynamics, climate prediction, oil exploration, etc. Therefore a systematic research and develop-ment of numerical methodology for Hamiltonian systems is well motivated. Were it successful, it would imply wide-ranging applications.

Features7 The symplectic geometric algorithm of K. Feng is unique 7 Classical, fundamental, and impor-tant reference in structure-preserving algorithm of computational mathematics 7 A must for the computational mathematician to understand the background, motivation, and the significance of the symplectic geometric algorithm

Fields of interestComputational Mathematics and Numerical Analysis; Geometry; Algebraic Topology

Target groupsUseful not only for numerical analysts, but also for those in theoretical physics, computational chemistry, celestial mechanics

A. Frazho, W. Bhosri, Purdue University, West Lafayette, IN, USA

An Operator Perspective on Signals and Systems

Features7 Uses geometric techniques to develop both the theory and the algorithms behind many factoriza-tion, interpolation, and signal processing problems arising in engineering and operator theory 7 Some “new” algorithms based on finite section methods are presented 7 Numerical examples using MATLAB are included

ContentsPreface.- I Basic Operator Theory.- 1 The Wold Decomposition.- 2 Toeplitz and Laurent Opera-tors.- 3 Inner and Outer Functions.- 4 Rational Inner and Outer Functions.- 5 The Naimark Representation.- 6 The Rational Case.- II Finite Section Techniques.- 7 The Levinson Algorithm and Factorization.- 8 Isometric Representations and Factorization.- 9 Signal Processing.- III Riccati Methods.- 10 Riccati Equations and Factorization.- 11 Kalman and Wiener Filtering.- IV Interpolation Theory.- 13 Contractive Nevanlinna-Pick Inter-polation.- V Appendices.- 14 A Review of State Space.- 15 The Levinson Algorithm.- Index.

Fields of interestOperator Theory; Systems Theory, Control; Computational Science and Engineering

Target groupsGraduate students and researchers in operator theory, control systems and signal processing


Mathematics

Due December 2009

Originally published in the series: Progress in Mathematics Vol 166

1st. ed 1998. 2nd printing 2010. Approx. 410 p. (Modern Birkhäuser Classics) Hardcover

7 € 39,95 | £35.997 * € (D) 42,75 | € (A) 43,95 | sFr 64,90ISBN 978-3-0346-0328-7

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Mathematics

Due November 2009

Distribution rights in China: Zhejiang Science and Technology Publishing House.

Jointly published with Zhejiang Science and Technology Publishing House.

2010. Approx. 640 p. 62 illus. Hardcover


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Mathematics

Due February 2010

2010. Approx. 445 p. Hardcover

7 € 99,00 | £89.007 * € (D) 105,93 | € (A) 108,90 | sFr 159,00ISBN 978-3-0346-0291-4

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S. R. Ghorpade, B. V. Limaye, Indian Institute of Technology, Bombay, Powai, Mumbai, India

A Course in Multivariate Calculus and Analysis

This self-contained textbook gives a thorough exposition of multivariable calculus. It can be viewed as a sequel to the one-variable calculus text, A Course in Calculus and Real Analysis, published in the same series. The emphasis is on correlating general concepts and results of multivariable calculus with their counterparts in one-variable calculus. For example, when the general definition of the volume of a solid is given using triple inte-grals, the authors explain why the shell and washer methods of one-variable calculus for computing the volume of a solid of revolution must give the same answer. Further, the book includes genuine analogues of basic results in one-variable calculus, such as the mean value theorem and the funda-mental theorem of calculus.

Features7 Self-contained, rigorous book of reasonable size 7 Neatly ties up multivariate calculus with its relics in one variable calculus 7 Caters to theo-retical as well as practical aspects of multivariate calculus 7 Follows a highly organized structure, where each chapter includes sections, subsections, notes and comments, and exercises

ContentsPreface.- Vectors and Functions.- Sequences, Continuity and Limits.- Partial and Total Differ-entiation.- Applications of Partial Differentiation.- Multiple Integration.- Applications and Approxi-mations of Multiple Integrals.- Double Series and Improper Double Integrals.- Appendix: The Change of Variables Formula.- References.- Index.

Fields of interestAnalysis

Target groupsAdvanced undergraduate students taking a course in multivariate calculus; also useful to advanced undergraduate and graduate students taking a course in real analysis

D. Hinrichsen, University of Bremen, Germany; A. J. Pritchard

Mathematical Systems

Theory IModelling, State Space Analysis, Stability and Robustness

This is the first volume of a book which presents the mathematical foundations of systems and control theory in a self-contained, comprehen-sive, detailed and mathematically rigorous way. This volume is devoted to the state space analysis of dynamical systems, whereas the 2nd volume will be devoted to control. It combines features of a detailed introductory textbook with that of a reference source. Throughout the book there are many examples and figures illustrating the text which help to bring out the intuitive ideas behind the mathematical constructions. It is accessible to mathematics students after two years of math-ematics and graduate engineering students special-izing in systems theory. The reader is gradually brought to the frontiers of research and on the way the required mathematical background material is developed with detailed proofs. As such the book will be useful for established researchers in systems theory as well as mathematicians and engineers interested in the mathematical foundations of systems and control.

Features7 Comprehensive coverage of an important field in applied mathematics

Fields of interestDynamical Systems and Ergodic Theory; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control

Target groupsResearchers and graduate students in systems theory

W. Hochstättler, Fernuni Hagen, Germany; A. Schliep, The State University of New Jersey, Piscataway, NJ, USA

CATBoxAn Interactive Course in Combinatorial Optimization

Graph algorithms are easy to visualize and indeed there already exists a variety of packages to animate the dynamics when solving problems from graph theory. Still it can be difficult to understand the ideas behind the algorithm from the dynamic display alone. CATBox consists of a software system for animating graph algorithms and a course book which we developed simultaneously. The software system presents both the algorithm and the graph and puts the user always in control of the actual code that is executed. In the course book, intended for readers at advanced undergraduate or graduate level, computer exercises and examples replace the usual static pictures of algorithm dynamics. For this volume we have chosen solely algo-rithms for classical problems from combinatorial optimization, such as minimum spanning trees, shortest paths, maximum flows, minimum cost flows, weighted and unweighted matchings both for bipartite and non-bipartite graphs. Find more information at http://schliep.org/CATBox/.

From the contents1 Discrete Problems from Applications.- 2 Basics, Notation and Data Structures.- 3 Minimum Span-ning Trees.- 4 Linear Programming Duality.- 5 Shortest Paths.- 6 Maximal Flows.- 7 Minimum-cost Flows.- 8 Matching.- 9 Weighted Matching.-

Fields of interestCombinatorics; Optimization; Operations Research, Mathematical Programming

Target groupsUndergraduate students in mathematics and computer science, advanced high school students, and students with a minor in either mathematics or computer science at any level


Mathematics

Due December 2009

2010. XII, 476 p. 79 illus., 76 in color. (Undergraduate Texts in Mathematics) Hardcover

7 € 59,95 | £53.997 * € (D) 64,15 | € (A) 65,95 | sFr 93,50ISBN 978-1-4419-1620-4

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Mathematics


1st ed. 2005. Corr. 2nd printing 2010. Approx. 805 p. (Texts in Applied Mathematics, Volume 48) Softcover

7 € 69,95 | £62.997 * € (D) 74,85 | € (A) 76,95 | sFr 109,00ISBN 978-3-642-03940-9

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Type of publicationUndergraduate textbook

Mathematics

Due November 2009

2010. XII, 190 p. Softcover

7 € 49,95 | £44.997 * € (D) 53,45 | € (A) 54,95 | sFr 77,50ISBN 978-3-540-14887-6

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M. Holz, K. Steffens, Universität Hannover, Germany; E. Weitz, Hamburg

Introduction to Cardinal Arithmetic

This book is an introduction into modern cardinal arithmetic in the frame of the axioms of Zermelo-Fraenkel set theory together with the axiom of choice. A first part describes the classical theory developed by Bernstein, Cantor, Hausdorff, König and Tarski between 1870 and 1930. Next, the development in the 1970s led by Galvin, Hajnal and Silver is characterized. The third part presents the fundamental investigations in pcf theory which have been worked out by Shelah to answer the questions left open in the 1970s.

From the reviews7 The book should be required reading for every advanced graduate student of set theory. Several courses at various levels could be based on the earlier chapters. There is a useful set of exercises at the end of most sections in the first four chapters 7 Mathematical Reviews

Features7 Self-contained introduction to cardinal arith-metic which also includes pcf theory 7 Gives a relatively complete survey of results provable in ZFC

ContentsFoundations.- The Galvin-Hajnal Theorem.- Ordinal Functions.- Approximation Sequences.- pcf-Theory.- Local Properties.- Applications.

Fields of interestMathematics, general

Target groupsUndergraduates, and also postgraduate students and researchers who want to broaden their knowl-edge of cardinal arithmetic

T. Linß, TU Dresden, Germany

Layer-Adapted Meshes for Reaction-Convection-Diffusion Problems

This book on numerical methods for singular perturbation problems – in particular, stationary reaction-convection-diffusion problems exhibiting layer behaviour is devoted to the construction and analysis of layer-adapted meshes underlying these numerical methods. A classification and a survey of layer-adapted meshes for reaction-convection-diffusion problems are included. This structured and comprehensive account of current ideas in the numerical analysis for various methods on layer-adapted meshes is addressed to researchers in finite element theory and perturba-tion problems. Finite differences, finite elements and finite volumes are all covered.

Contents1 Introduction.- 2 Layer-adapted meshes.- Part I One dimensional problems.- 3 The analytical behaviour of solutions.- 4 Finite difference schemes for convection-diffusion problems.- 5 Finite element and finite volume methods.- 6 Discretisations of reaction-convection-diffusion problems.- Part II Two dimensional problems.- 7 The analytical behaviour of solutions.- 8 Reac-tion-diffusion problems.- 9 Convection-diffusion problems.

Fields of interestNumerical Analysis; Ordinary Differential Equa-tions; Partial Differential Equations

Target groupsResearchers and graduate students in mathematics and computer science

W. Liu, University of Central Arkansas, Conway, AR, USA

Elementary Feedback Stabilization of the Linear Reaction-convection-diffusion Equation and the Wave Equation

This book addresses the feedback stabilization of the linear reaction-convection-diffusion equa-tion and the linear wave equation. Both interior and boundary control problems are discussed. Methods employed to handle the problems include the eigenfunction expansion, integral transform, perturbed energy method, and optimal control technique. These powerful methods are frequently used for solving control problems of partial differ-ential equations. Unlike the existing advanced control theory books written in an abstract setting, this book presents control theory by means of concrete examples. Therefore, this book is easy to read. Once readers learn about the ideas and methods from these concrete control examples, they can apply them to solve other control prob-lems of partial differential equations.

Fields of interestPartial Differential Equations; Applications of Mathematics; Control

Target groupsResearchers and professionals


Mathematics

Due December 2009

Originally published in the series: Birkhäuser Advanced Texts

1st ed.1999. 2nd printing 2010. Approx. 310 p. (Modern Birkhäuser Classics) Hardcover

7 € 34,95 | £31.997 * € (D) 37,40 | € (A) 38,45 | sFr 59,90ISBN 978-3-0346-0327-0

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Mathematics

Due December 2009

2009. XII, 310 p. (Lecture Notes in Mathematics, Volume 1985) Softcover

7 € 69,95 | £62.997 * € (D) 74,85 | € (A) 76,95 | sFr 109,00ISBN 978-3-642-05133-3

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Mathematics

Due November 2009

2010. X, 300 p. (Mathématiques et Applications, Volume 66) Softcover

7 € 89,95 | £81.007 * € (D) 96,25 | € (A) 98,95 | sFr 140,00ISBN 978-3-642-04612-4

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A. Lubotzky, Hebrew University, Jerusalem, Israel

Discrete Groups, Expanding Graphs and Invariant Measures

Appendix by: J. D. Rogawski

The book presents the solutions to two problems: the first is the construction of expanding graphs – graphs which are of fundamental importance for communication networks and computer science; the second is the Ruziewicz problem concerning the finitely additive invariant measures on spheres. The author, who played an important role in these developments, explains the two problems and their solutions from a perspective which reveals why all these seemingly unrelated topics are so intercon-nected. The unified approach shows interrelations between different branches of mathematics such as graph theory, measure theory, Riemannian geom-etry, discrete subgroups of Lie groups, representa-tion theory and analytic number theory. Special efforts were made to make the book accessible to graduate students in mathematics and computer science. A number of problems and suggestions for further research are presented.

Features7 Award-winning monograph of the Ferran Sunyer i Balaguer Prize 1993 7 Exciting tour through several areas of mathematics 7 Recent mathematical research

Fields of interestGroup Theory and Generalizations; Real Func-tions; Number Theory

Target groupsResearchers, graduate students in mathematics and computer science

M. Luptácik, Vienna University of Economics and Business Administration, Vienna, Austria

Mathematical Optimization and Economic Analysis

“Mathematical Optimization and Economic Analysis” is a self-contained introduction to various optimization techniques used in economic modeling and analysis such as geometric, linear, and convex programming and data envelopment analysis. Through a systematic approach, this book demonstrates the usefulness of these mathematical tools in quantitative and qualitative economic analysis. The book presents specific examples to demon-strate each technique’s advantages and applica-bility as well as numerous applications of these techniques to industrial economics, regulatory economics, trade policy, economic sustainability, production planning, and environmental policy.

Features7 A detailed presentation of both single-objective and multiobjective optimization 7 An in-depth exposition of various applied optimization prob-lems 7 Implementation of optimization tools to improve the accuracy of various economic models 7 Extensive resources suggested for further reading

ContentsPart I Single-Objective Optimization.- 1. Scarcity and Efficiency.- 2. Kuhn–Tucker Conditions.- 3. Convex Programming.- 4. Linear Program-ming.- 5. Data Envelopment Analysis.- 6. Geometric Programming.- Part II Multiobjec-tive Optimization.- 7. Fundamentals of Multiob-jective Optimization.- 8. Multiobjective Linear Programming.

Fields of interestOptimization; Economic Theory; Operations Research/Decision Theory

Target groupsGraduate and postgraduate students studying quantitative economics, economics researchers and applied mathematicians

K. Marathe, City University of New York, Brooklyn, NY, USA

Topics in Physical Mathematics

Features7 A self-contained book that includes the basic material in physics and mathematics, prior to a discussion of their interaction 7 Demonstrates how various physical theories have played a crucial role in recent developments in mathematics, in particular, in geometric topology 7 Theories that are not yet accepted as physical theories are used, when they have led to new ideas and results in mathematics

ContentsAlgebra.- Topology.- Manifolds.- Bundles and Connections.- Characteristic Classes.- Theory of Fields, I: Classical.- Theory of Fields, II: Quantum and Topological.- Yang-Mills-Higgs Fields.- 4-Manifold Invariants.- 3-Manifold Invariants.- Knot and Link Invariants.- Dictionary of Termi-nology.- Historical and Biographical Notes.- Cate-gories and Chain Complexes.- Operator Theory.

Fields of interestDifferential Geometry; Manifolds and Cell Complexes (incl. Diff.Topology); Topology



Mathematics

Due December 2009


1st ed. 1994. 2nd printing 2010. Approx. 210 p. (Modern Birkhäuser Classics) Hardcover

7 € 34,95 | £31.997 * € (D) 37,40 | € (A) 38,45 | sFr 59,90ISBN 978-3-0346-0331-7

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Mathematics

Due December 2009

2010. XIV, 292 p. 53 illus. (Springer Optimization and Its Applications, Volume 36) Hardcover

7 € 79,95 | £72.007 * € (D) 85,55 | € (A) 87,95 | sFr 124,50ISBN 978-0-387-89551-2

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Mathematics

Due February 2010

2010. Approx. 460 p. Hardcover


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J. Matousek, Charles University, Praha, Czech Republic

Geometric DiscrepancyAn Illustrated Guide

What is the “most uniform” way of distributing n points in the unit square? How big is the “irregu-larity” necessarily present in any such distribution? Such questions are treated in geometric discrep-ancy theory. The book is an accessible and lively introduction to this area, with numerous exercises and illustrations. In separate, more specialized parts, it also provides a comprehensive guide to recent research. Including a wide variety of mathematical techniques (from harmonic analysis, combinatorics, algebra etc.) in action on non-trivial examples, the book is suitable for a “special topic” course for early graduates in mathematics and computer science. Besides professional mathematicians, it will be of interest to specialists in fields where a large collection of objects should be “uniformly” represented by a smaller sample (such as high-dimensional numerical integration in computational physics or financial mathematics, efficient divide-and-conquer algorithms in computer science, etc.).

Features7 Only up-to-date comprehensive guide to the subject

ContentsIntroduction.- Low-Discrepancy Sets for Axis-Parallel Boxes.- Upper Bounds in the Lebesgue-Measure Setting.- Combinatorial Discrep-ancy.- VC-Dimension and Discrepancy.- Lower Bounds.- More Lower Bounds and the Fourier Transform.- Tables of Selected Discrepancy Bounds.- Bibliography.- Index.- Hints.

Fields of interestGeometry; Combinatorics

Target groupsGraduate students and researchers in mathematics and computer science

J. D. Monk, University of Colorado, Boulder, CO, USA

Cardinal Invariants on Boolean Algebras

This book is concerned with cardinal number valued functions defined for any Boolean algebra. Examples of such functions are independence, which assigns to each Boolean algebra the supremum of the cardinalities of its free subalge-bras, and cellularity, which gives the supremum of cardinalities of sets of pairwise disjoint elements. The questions considered are the behaviour of these functions under algebraic operations such as products, free products, ultraproducts, and their relationships to one another. Assuming familiarity with only the basics of Boolean algebras and set theory, through to simple infinite combinatorics and forcing, the book reviews current knowledge about these functions, giving complete proofs for most facts. A special feature of the book is the attention given to open problems, of which 97 are formulated.

Features7 Covers most of what was known on cardinal invariants in Boolean algebras 7 List of 97 inter-esting open problems

From the contentsSpecial operations on Boolean algebras.- Special classes of Boolean algebras.- Cellularity.- Depth.- Topological density.- pi-weight.- Length.- Irre-dundance.- Cardinality.- Independence.- pi-char-acter.- Tightness.- Spread.- Character.- Hereditary Lindelöf degree.- Hereditary density.- Incompara-bility.- Hereditary cofinality.

Fields of interestMathematical Logic and Foundations; Order, Lattices, Ordered Algebraic Structures


K. Murota, Kyoto University, Kyoto, Japan

Matrices and Matroids for Systems Analysis

A matroid is an abstract mathematical structure that captures combinatorial properties of matrices. This book offers a unique introduction to matroid theory, emphasizing motivations from matrix theory and applications to systems analysis. This book serves also as a comprehensive presentation of the theory and application of mixed matrices, developed primarily by the present author in the 1990’s. A mixed matrix is a convenient mathematical tool for systems analysis, compatible with the physical observation that “fixed constants” and “system parameters” are to be distinguished in the description of engineering systems. This book will be extremely useful to graduate students and researchers in engineering, math-ematics and computer science.

From the reviews7 …The book has been prepared very carefully, contains a lot of interesting results and is highly recommended for graduate and postgraduate students 7 András Recski, Mathematical Reviews Clippings 2000m:93006

Features7 First comprehensive presentation of the theory and application of mixed matrices and a unique introduction to matroid theory 7 Self-contained presentation of the theory and applications of matroids, written in such a way that the reader can acquire familiarity with matroids through matrices and reach the stage of understanding the most recent results in matroid theory

Fields of interestCombinatorics; Linear and Multilinear Algebras, Matrix Theory; Appl. Mathematics/Computational Methods of Engineering

Target groupsGraduate students and researchers in mathematics


Mathematics

Due December 2009Previously announced in Springer News 10/2009

1st ed. 1999. 2nd printing 2010. XI, 288 p. (Algorithms and Combinatorics, Volume 18) Softcover

7 € 79,95 | £72.007 * € (D) 85,55 | € (A) 87,95 | sFr 124,50ISBN 978-3-642-03941-6

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Mathematics

Due November 2009


1st ed. 1996. 2nd printing 2010. Approx. 330 p. (Modern Birkhäuser Classics) Softcover

7 € 32,66 | £29.997 * € (D) 34,95 | € (A) 35,93 | sFr 59,90ISBN 978-3-0346-0333-1

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Mathematics


1st ed. 2000. 2nd printing 2010. XII, 483 p. 64 illus. (Algo-rithms and Combinatorics, Volume 20) Softcover

7 € 89,95 | £81.007 * € (D) 96,25 | € (A) 98,95 | sFr 140,00ISBN 978-3-642-03993-5

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H. Oertel, University of Karlsruhe, Germany (Ed.)

Prandtl-Essentials of Fluid Mechanics

Translated by: K. Asfaw With contributions by: P. Erhardt, D. Etling, U. Muller, U. Riedel, K. Sreenivasan, J. Warnatz

This book is an update and extension of the classic textbook by Ludwig Prandtl, Essentials of Fluid Mechanics. It is based on the 12th German edition with additional material included. Chapters on wing aerodynamics, heat transfer, and layered flows have been revised and extended, and there are new chapters on fluid mechanical instabilities and biomedical fluid mechanics. References to the literature have been kept to a minimum, and the extensive historical citations may be found by referring to previous editions. This book is aimed at science and engineering students who wish to attain an overview of the various branches of fluid mechanics. It will also be useful as a reference for researchers working in the field of fluid mechanics.

Features7 Ludwig Prandtl has been called the “father” of modern fluid mechanics 7 Expanded version of Prandtl’s original text, which is a classic in the field of fluid mechanics

ContentsPreface.- Introduction.- Properties of Liquids and Gases.- Kinematics of Fluid Flow.- Dynamics of Fluid Flow.- Fundamental Equations of Fluid Mechanics.- Instabilities and Turbulent Flows.- Convective Heat and Mass Transfer.- Multiphase Flows.- Reactive Flows.- Flows in the Atmo-sphere and in the Ocean.- Microflows.- Biofluid Mechanics.- Selected Bibliography.- Index.

Fields of interestClassical Continuum Physics; Theoretical, Math-ematical and Computational Physics; Appl. Math-ematics/Computational Methods of Engineering

Target groupsSenior undergraduates, graduate students, researchers

N. M. Patrikalakis, Massachussetts Institute of Technology, Cambridge, MA, USA; T. Maekawa, Yokohama National University, Japan

Shape Interrogation for Computer Aided Design and Manufacturing

Shape interrogation is the process of extraction of information from a geometric model. It is a fundamental component of Computer Aided Design and Manufacturing (CAD/CAM) systems. The authors focus on shape interrogation of geometric models bounded by free-form surfaces. Free-form surfaces, also called sculptured surfaces, are widely used in the bodies of ships, automobiles and aircraft, which have both functionality and attractive shape requirements. Many electronic devices as well as consumer products are designed with aesthetic shapes, which involve free-form surfaces. This book provides the mathematical fundamentals as well as algorithms for various shape interrogation methods.

From the reviews7 … there are several excellent books in the area of geometric modeling and … solid modeling. The major contribution of this book lies in its skilful manner of providing a bridge between these two areas that is guaranteed to make the target audience cry out aloud with delight 7 Current Engineering Practice 2002-2003

Features7 Two top authors of MIT present a textbook on CAD and geometrical modeling 7 One of the few textbooks in the field

Fields of interestVisualization; Manufacturing, Machines, Tools; Mechanical Engineering

Target groupsGraduate students in mathematics, engineering, computer science, focusing on geometrical model-ling and solid modelling

M. Peters, Springer-Verlag, Mathematics Editorial I, Heidelberg, Germany (Ed.)

Computational Fluid Dynamics for Sport Simulation

All over the world sport plays a prominent role in society: as a leisure activity for many, as an ingre-dient of culture, as a business and as a matter of national prestige in such major events as the World Cup in soccer or the Olympic Games. Hence, it is not surprising that science has entered the realm of sports, and, in particular, that computer simulation has become highly relevant in recent years. This is explored in this book by choosing five different sports as examples, demonstrating that compu-tational science and engineering (CSE) can make essential contributions to research on sports topics on both the fundamental level and, eventually, by supporting athletes’ performance.

Fields of interestComputational Science and Engineering; Appl. Mathematics/Computational Methods of Engi-neering; Mathematics of Computing

Target groupsComputational scientists, physicists and engineers dealing with sports simulation, sports scientists


Physics and Astronomy

Due November 2009

3rd ed. 2010. X, 740 p. (Applied Mathematical Sciences, Volume 158) Hardcover

7 € 69,95 | £62.997 * € (D) 74,85 | € (A) 76,95 | sFr 109,00ISBN 978-1-4419-1563-4

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Mathematics

Due November 2009

1st ed. 2002, 2nd corr. printing. 2010. XVI, 408 p. 173 illus., 8 in color. Softcover

7 € 59,95 | £53.997 * € (D) 64,15 | € (A) 65,95 | sFr 93,50ISBN 978-3-642-04073-3

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Mathematics

Due December 2009

2009. VII, 200 p. (Lecture Notes in Computational Science and Engineering, Volume 72) Hardcover


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H. Pottmann, KAUST, Saudi Arabia, and Technical University of Vienna, Austria; J. Wallner, Technical University of Graz, Austria

Computational Line Geometry

The geometry of lines occurs naturally in such different areas as sculptured surface machining, computation of offsets and medial axes, surface reconstruction for reverse engineering, geomet-rical optics, kinematics and motion design, and modeling of developable surfaces. This book covers line geometry from various viewpoints and aims towards computation and visualization. Besides applications, it contains a tutorial on projective geometry and an introduction into the theory of smooth and algebraic manifolds of lines. It will be useful to researchers, graduate students, and anyone interested either in the theory or in computational aspects in general, or in applica-tions in particular.

From the reviews7 The authors have combined results from the classical parts of geometry with computational methods. This results in a unique and fascinating blend... The contents of the book are visualized by a wealth of carefully chosen illustrations, making the book a sheer pleasure to read 7 B.Jüttler, MATH.REVIEWS 2002

Features7 For the first time studies line geometry from the viewpoint of scientific computation 7 Shows the interplay between theory and numerous applications

Fields of interestGeometry; Computational Mathematics and Numerical Analysis; Visualization

Target groupsMathematicians, computer scientists, and engineers working in geometrical modelling and visualization

V. V. Prasolov, Independent University of Moscow, Russia

PolynomialsTranslated by: D. Leites

From the reviews7 ... Despite the appearance [...] in a series titled Algorithms and Computation of Mathematics, computation occupies only a small part of the monograph. It is best described as a useful refer-ence for one’s personal collection and a text for a full-year course given to graduate or even senior undergraduate students. [...] the book under review is worth purchasing for the library and possibly even for one’s own collection. The author’s interest in the history and development of this area is evident, and we have pleasant glimpses of progress over the last three centuries [...] the reader gains a synopsis of and guide to the literature ... 7 E.Barbeau, SIAM Review 47:3, 2005 7 This is an exposition of polynomial theory and results, both classical and modern. [...] the volume is packed with results and proofs that are well organ-ised thematically [...] What is unusual is to have a text that embraces and intermingles both analytic and algebraic aspects of the theory… 7 S.D.Cohen, Math.Reviews 2005

Features7 Covers its topic in greater depth than the typical standard books on polynomial algebra

From the contentsRoots of Polynomials.- Irreducible Polynomials.- Polynomials of a Particular Form.- Certain Properties of Polynomials.- Galois Theory.- Ideals in Polynomial Rings.

Fields of interestAlgebra

Target groupsGraduate students, lecturers and researchers in mathematics

R. Rannacher, University of Heidelberg, Germany; A. Sequeira, Instituto Superior Técnico/UTL, Lisboa, Portugal (Eds.)

Advances in Mathematical Fluid MechanicsDedicated to Giovanni Paolo Galdi on the Occasion of his 60th Birthday

This book is a unique collection of high-level papers devoted to fundamental topics in math-ematical fluid mechanics and their applications, mostly in connection with the scientific work of Giovanni Paolo Galdi. The contributions are mainly centered on the study of the basic proper-ties of the Navier-Stokes equations, including existence, uniqueness, regularity, and stability of solutions. Related models describing non-Newto-nian flows, turbulence, and fluid-structure interac-tions are also addressed. The results are analytical, numerical and experimental in nature, making the book particularly appealing to a vast readership encompassing mathematicians, engineers and physicists. The diversity of the topics, in addition to the different approaches, will provide readers a global and up-to-date overview of both the latest findings on the subject and of the salient open questions.

Fields of interestApplications of Mathematics; Classical Continuum Physics; Computational Mathematics and Numerical Analysis

Target groupsComputational scientists, physicists, numerical analysts


Mathematics


1st ed. 2001. 2nd printing 2010. IX, 563 p. 264 illus., 17 in color. (Mathematics and Visualization) Softcover

7 € 99,95 | £90.007 * € (D) 106,95 | € (A) 109,95 | sFr 155,50ISBN 978-3-642-04017-7

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Mathematics

AvailablePreviously announced in Springer News 10/2009

Original Russian edition published by Moscow Center for Continuous Math. Education, 2001

1st ed. 2004, 2nd printing 2009. XIII, 301 p. 8 illus. (Algorithms and Computation in Mathematics, Volume 11) Softcover

7 € 59,95 | £53.997 * € (D) 64,15 | € (A) 65,95 | sFr 93,50ISBN 978-3-642-03979-9

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Mathematics

Due December 2009Previously announced in Springer News 10/2009

2010. XII, 570 p. Hardcover

7 € 129,95 | £117.007 * € (D) 139,05 | € (A) 142,95 | sFr 202,00ISBN 978-3-642-04067-2

9<HTOGPC=aeaghc>





W. Rautenberg, Freie Universität Berlin, Germany

A Concise Introduction to Mathematical Logic

Traditional logic as a part of philosophy is one of the oldest scientific disciplines and can be traced back to the Stoics and to Aristotle. Mathematical logic, however, is a relatively young discipline and arose from the endeavors of Peano, Frege, and others to create a logistic foundation for math-ematics. It steadily developed during the twentieth century into a broad discipline with several sub-areas and numerous applications in mathematics, informatics, linguistics and philosophy. This book treats the most important material in a concise and streamlined fashion. The third edition is a thorough and expanded revision of the former. Although the book is intended for use as a graduate text, the first three chapters can easily be read by undergraduates interested in mathematical logic. These initial chapters cover the material for an introductory course on mathematical logic, combined with applications of formalization tech-niques to set theory. Chapter 3 is partly of descrip-tive nature, providing a view towards algorithmic decision problems, automated theorem proving, non-standard models including non-standard analysis, and related topics.

Features7 Chapter summaries 7 Section summaries 7 Detailed illustrations 7 Study guides at the ends of sections 7 Exercises at the ends of chap-ters or sections 7 Solutions to selected exercises in the book 7 A separate solutions manual (on the Internet) 7 Instructor’s manual with solutions and teaching guides

From the contentsPropositional Logic.- First-Order Logic.- Complete Logical Calculi.- Foundations of Logical Program-ming.- Elements of Model Theory.

Fields of interestMathematical Logic and Foundations; Computa-tional Science and Engineering


A. L. Rosenberg, Colorado State University and Distinguished University Professor Emeritus Univer-sity of Massachusetts, Amherst, MA, USA

The Pillars of Computation TheoryState, Encoding, Nondeterminism

The abstract branch of theoretical computer science known as Computation Theory typically appears in undergraduate academic curricula in a form that obscures both the mathematical concepts that are central to the various compo-nents of the theory and the relevance of the theory to the typical student. This regrettable situation is due largely to the thematic tension among three main competing principles for organizing the material in the course. This book is motivated by the belief that a deep understanding of, and operational control over, the few “big” mathematical ideas that underlie Computation Theory is the best way to enable the typical student to assimilate the “big” ideas of Computation Theory into her daily computational life.

Features7 Large selection of exercises 7 Presents a unique approach to computation theory

ContentsPreface and Manifesto.- Introduction.- Mathemat-ical Preliminaries.- State.- Encoding.- Nondeter-minism.- Bibliography.

Fields of interestComputational Mathematics and Numerical Analysis

Target groupsAdvanced undergrads in math and computer science

Z. Schuss

Theory and Applications of Stochastic ProcessesAn Analytical Approach

Stochastic processes and diffusion theory are the mathematical underpinnings of many scientific disciplines, including statistical physics, physical chemistry, molecular biophysics, communica-tions theory and many more. Many books, reviews and research articles have been published on this topic, from the purely mathematical to the most practical. This book offers an analytical approach to stochastic processes that are most common in the physical and life sciences, as well as in optimal control and in the theory of filltering of signals from noisy measurements. Its aim is to make prob-ability theory in function space readily accessible to scientists trained in the traditional methods of applied mathematics, such as integral, ordinary, and partial differential equations and asymptotic methods, rather than in probability and measure theory.

Features7 A wealth of examples from physics, chem-istry, biology and engineering 7 Treads a route between probabilists and physical scientists 7 Includes many physically relevant results and discussions

From the contentsThe Physical Brownian Motion: Diffusion and Noise.- The Probability Space of Brownian Motion.- Ito Integration and Calculus.- Stochastic Differential Equations.- The Discrete Approach and Boundary Behavior.- The First Passage Time of Diffusions.

Fields of interestProbability Theory and Stochastic Processes; Statistical Physics, Dynamical Systems and Complexity; Appl. Mathematics/Computational Methods of Engineering

Target groupsBeginning graduates in applied mathematics, physics, biologists, engineering, mechanical


Mathematics

Due December 2009

3rd ed. 2010. Approx. 340 p. 25 illus. (Universitext) Softcover


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Mathematics

Due November 2009

2010. Approx. 340 p. 49 illus. (Universitext) Softcover


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Mathematics

Due January 2010

2010. X, 356 p. (Applied Mathematical Sciences, Volume 170) Hardcover


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G. Shimura, Princeton University, Princeton, NJ, USA

Arithmetic of Quadratic Forms

This book is divided into two parts. The first part is preliminary and consists of algebraic number theory and the theory of semisimple algebras. There are two principal topics: classification of quadratic forms and quadratic diophantine equa-tions. The first topic is further divided into two types of theories: classification over an algebraic number field and classification over the ring of algebraic integers. To ensure the book would be concise, the author proved basic theorems in local class field theory only in some special cases, and the Hilbert reci-procity law only over the rational number field. However, the author stated the main theorems with an arbitrary number field as the base field, so the reader familiar with class field theory will be able to learn the arithmetic theory of quadratic forms with no further references.

Features7 Discusses algebraic number theory and the theory of semisimple algebras 7 Discusses clas-sification over an algebraic number field and clas-sification over the ring of algebraic integers 7 Discusses local class field theory

ContentsPreface.- Notation and Terminology.- The Quadratic Reciprocity Law.- Arithmetic in an Algebraic Number Field.- Various Basic Theo-rems.- Algebras Over a Field.- Quadratic Forms Over a Field.- Deeper Arithmetic of Quadratic Forms.- Quadratic Diophantine Equations.- Refer-ences.- Index.

Fields of interestAlgebra; Number Theory; General Algebraic Systems

Target groupsGraduate students; professionals

S. A. Steinberg, University of Toledo, OH, USA

Lattice-ordered Rings and Modules

From the reviews7 Lattice-ordered rings and modules are of interest both to algebraists and to functional analysts. Previous authors have presented only those results that are needed for the applications that they have in mind. Having a book like this one would be a great boon. Both the algebraists and the analysts would benefit from having the fundamental results all gathered together in one book. This book would fill in the gap admirably. Any algebraist or functional analyst whose work involves ordered structures would be interested in this book. That includes mathematicians who study: lattices, ordered semigroups, ordered groups, ordered rings, ordered fields, Riesz spaces, vector lattices, or Banach lattices. It would also be useful for math-ematicians who are interested in general ring theory, general group theory, matrix algebras, or function algebras (especially Banach algebras). In short, there is a wide audience who would find the tools that this book provides very useful ...

Features7 Clearly written and self-contained 7 Each chapter contains a wealth of exercises as well as historical notes 7 Provides a comprehensive summary of the past 60 years of research in this field

ContentsPreface.- Partially Ordered Sets and Lattices.- Lattice-Ordered Groups.- Lattice-Ordered Rings.- The Category of f-modules.- Fields.- Additional Topics.- Index.- References.

Fields of interestOrder, Lattices, Ordered Algebraic Structures; Algebra; Non-associative Rings and Algebras

Target groupsGraduate students and researchers in the field of lattice theory, ring theory, or ordered fields

L. Tartar, Carnegie Mellon University, Pittsburgh, PA, USA

The General Theory of HomogenizationA Personlized Introduction

Contents1 Why Do I Write?- 2 A Personalized Overview of Homogenization I.- 3 A Personalized Overview of Homogenization II.- 4 An Academic Question of Jacques-Louis Lions.- 5 A Useful Generalization by Francois Murat .- 6 Homogenization of an Elliptic Equation .- 7 The Div-Curl Lemma.- 8 Physical Implications of Homogenization.- 9 A Framework with Differential Forms.- 10 Properties of H-convergence.- 11 Homogenization of Mono-tone Operators.- 12 Homogenization of Laminated Materials.- 13 Correctors in Linear Homogeniza-tion.- 14 Correctors in Nonlinear Homogeniza-tion.- 15 Holes with Dirichlet Conditions.- 16 Holes with Neumann Conditions.- 17 Compen-sated Compactness.- 18 A Lemma for Studying Boundary Layers.- 19 A Model in Hydrody-namics.- 20 Problems in Dimension N = 2.- 21 Bounds on Eective Coefficients.- 22 Functions Attached to Geometries .- 23 Memory Effects.- 24 Other Nonlocal Effects.- 25 The Hashin-Shtrikman Construction.- 26 Confocal Ellipsoids and Spheres.- 27 Laminations Again, and Again.- 28 Wave Front Sets, H-Measures.- 29 Small-Amplitude Homogenization.- 30 H-Measures and Bounds on Effective Coeffcients.- 31 H-Measures and Propagation Effects.- 32 Variants of H-Measures.- 33 Relations Between Young Measures and H-Measures.- 34 Conclusion.- 35 Biographical Information.- 36 Abbreviations and Mathematical Notation.

Fields of interestPartial Differential Equations; Mechanics; Engineering Fluid Dynamics

Target groupsResearchers and graduate students in mathematics, continuum mechanics and physicsType of publication

Monograph

Mathematics

Due December 2009

2010. Approx. 260 p. (Springer Monographs in Mathematics) Hardcover


9<HTMEPB=jbhdbh>


Mathematics

Due December 2009

2010. XVIII, 630 p. 61 illus. Hardcover

7 € 64,95 | £58.997 * € (D) 69,50 | € (A) 71,45 | sFr 101,00ISBN 978-1-4419-1720-1

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Mathematics

Due December 2009

2009. XVIII, 434 p. (Lecture Notes of the Unione Matematica Italiana, Volume 7) Softcover

7 € 69,95 | £62.997 * € (D) 74,85 | € (A) 76,95 | sFr 109,00ISBN 978-3-642-05194-4

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W. Tucker, University of Uppsala, Sweden

Auto-Validating Numerical Methods

The main goal of this text is to introduce the reader to the field of auto-validating algorithms by providing a theoretical foundation supplemented with illuminating examples. The target audience is undergraduate or graduate students new to the field. Some knowledge of programming is useful, but not strictly necessary. The restriction to the one-dimensional setting is a conscious one. It allows us to focus exclusively on simple, but yet interesting problems, without too much math-ematical framework. The computer excersises are intended to “force” the reader into actually discov-ering how simple it is to implement the methods, and to solve numerical problems with rigour.

Features7 Self-contained with respect to the underlying mathematics/computer arithmetic 7 Includes small „program snippets” used to illustrate basic points 7 Nice spread of application areas (opti-mization, quadrature, ODEs etc)

From the contents1 Computer arithmetic: 1.1 Positional systems.- 1.2 Floating point numbers .- 1.3 Rounding.- 1.4 Floating point arithmetic.- 1.5 The IEEE stan-dards.- 1.6 Examples of floating point computa-tions.- 1.7 Computer Lab II.- 2 Interval arithmetic: 2.1 Real intervals.- 2.2 Real interval arithmetic.- 2.3 Extended interval arithmetic.- 2.4 Containment sets.- 3 Interval analysis: 3.1 Interval functions.- 3.2 Centered forms.- 3.3 Monotonicity.- 3.4 Computer Lab II.- 4 Auto-matic differentiation: 4.1 First-order derivatives.

Fields of interestComputational Mathematics and Numerical Analysis; Numerical Analysis; Ordinary Differen-tial Equations

Target groupsAdvanced undergraduate or beginning graduate students, engineers, mathematicians

A. Voros, CEA Saclay, Gif-sur-Yvette, France

Zeta Functions over Zeros of Zeta Functions

The famous zeros of the Riemann zeta function and its generalizations (L-functions, Dedekind and Selberg zeta functions) are analyzed through several zeta functions built over those zeros. These ‘second-generation’ zeta functions have surprisingly many explicit, yet largely unnoticed properties, which are surveyed here in an acces-sible and synthetic manner, and then compiled in numerous tables. No previous book has addressed this neglected topic in analytic number theory. Concretely, this handbook will help anyone faced with symmetric sums over zeros like Riemann’s. More generally, it aims at reviving the interest of number theorists and complex analysts toward those unfamiliar functions, on the 150th anniver-sary of Riemann’s work.

Contents1 Introduction.- 2 Infinite products and zeta-regularization.-3 The Riemann zeta function ζ (x) - a primer.- 4 Riemann zeros and factorizations of the zeta function.- 5 Superzeta functions: an overview.- 6 Explicit Formulae.- 7 The family of the 1st kind {Z (s | t)}.- 8 The family of the 2nd kind {Z (σ | t}.- 9 The family of the 3rd kind {Z(s |τ)}.- 10 Extension to other zeta- and L-functions.- 11 Application: an asymptotic criterion for the Riemann Hypothesis.-A Numerical explorations.- B The Selberg case.- C On the logarithmic deriva-tives at 1/2.- D On the zeros of the zeta function by Hj. Mellin (1917).- References.- Index.

Fields of interestNumber Theory; Functions of a Complex Variable; Approximations and Expansions

Target groupsResearchers and graduate students in analytic number theory, complex analysis in one variable, special functions and integral transforms

L. Y. Wang, G. G. Yin, Wayne State University, Detroit, MI, USA; J. Zhang, Y. Zhao, Chinese Academy of Sciences, Beijing, China

System Identification with Quantized Observations

The ability to identify systems in which only quantized output observations are available is often extremely important in real-world situa-tions. Due to sensor limitations, signal quantiza-tion, or coding for communications, many older methodologies fall short in building dynamic models from these observations. This work presents new methodologies that utilize quantized information in system identification and explores their potential in extending control capabilities for systems with limited sensor information or networked systems. The results of these meth-odologies can be applied to systems and control design, communication and computer networks, signal processing, sensor networks, mobile agents, data fusion, remote sensing, telemedicine, and any field in which noise-corrupted quantized data need to be processed.

Features7 First monograph dedicated to quantized identi-fication in systems 7 Applications to communi-cation and computer networks, signal processing, sensor networks, mobile agents, data fusion, remote sensing, telemedicine 7 For a broad audience of graduate students, systems theorists, control engineers, applied mathematicians, as well as practitioners who use identification algorithms in their work

Fields of interestSystems Theory, Control; Control; Algorithms

Target groupsGraduate students, practitioners and researchers in systems theory, control engineering, applied mathematics


Mathematics

Due March 2010

2010. XII, 170 p. (Frontiers in Mathematics) Softcover

7 € 29,95 | £26.997 * € (D) 32,05 | € (A) 32,95 | sFr 49,90ISBN 978-3-0346-0301-0

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Mathematics

Due December 2009

2009. XVIII, 159 p. (Lecture Notes of the Unione Matematica Italiana, Volume 8) Softcover

7 € 34,95 | £31.997 * € (D) 37,40 | € (A) 38,45 | sFr 54,50ISBN 978-3-642-05202-6

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Mathematics

Due March 2010

2010. Approx. 295 p. 40 illus. (Systems & Control: Foun-dations & Applications) Hardcover


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B. A. Wehrfritz, School of Mathematical Sciences, University of London, Queen Mary, London, UK

Group and Ring Theoretic Properties of Polycyclic Groups

Polycyclic groups are built from cyclic groups in a specific way. They arise in many contexts within group theory itself but also more generally in algebra, for example in the theory of Noetherian rings. They also touch on some aspects of topology, geometry and number theory. In roughly the first half of the book we develop the standard group theoretic techniques for studying polycyclic groups and the basic properties of these groups. In its second half this book is the first to focus specifically on the ring theoretic properties of polycyclic groups and their applications, often to purely group theoretic situations. The book is not intended to be encyclopedic. Instead, it is a study manual for graduate students and researchers coming into contact with polycy-clic groups, where the main lines of the subject can be learned from scratch. We do assume that the reader has been exposed to some undergraduate algebra, especially groups, rings and vector spaces. Thus it has been kept short and readable with a view that it can be read and worked through from cover to cover. At the end of each topic covered there is a description without proofs, but with full references, of further developments in the area. The book concludes with an extensive bibliography of items relating to polycyclic groups.

Fields of interestGroup Theory and Generalizations; Associative Rings and Algebras; Commutative Rings and Algebras

Target groupsMSc students, MPhil, PhD students, researchers

A. Yagi, Osaka University, Suita, Japan

Abstract Parabolic Evolution Equations and their Applications

The semigroup methods are known as a powerful tool for analyzing nonlinear diffusion equations and systems. The author has studied abstract para-bolic evolution equations and their applications to nonlinear diffusion equations and systems for more than 30 years. He gives first, after reviewing the theory of analytic semigroups, an overview of the theories of linear, semilinear and quasilinear abstract parabolic evolution equations as well as general strategies for constructing dynamical systems, attractors and stable-unstable manifolds associated with those nonlinear evolution equa-tions. In the second half of the book, he shows how to apply the abstract results to various models in the real world focusing on various self-organization models: semiconductor model, activator-inhibitor model, B-Z reaction model, forest kinematic model, chemotaxis model, termite mound building model, phase transition model, and Lotka-Volterra competition model. The process and techniques are explained concretely in order to analyze nonlinear diffusion models by using the methods of abstract evolution equations.

Features7 Fills the gaps of existing literature 7 Presents rigorous mathematical theories 7 Applies results focusing on various self-organization models 7 Author has studied abstract parabolic evolution equations and their applications to nonlinear diffu-sion equations and systems for more than 30 years

Fields of interestPartial Differential Equations; Dynamical Systems and Ergodic Theory; Mathematical Biology in General

Target groupsGraduate students and researchers in mathematics, mathematical biology, mathematical ecology, and science of self-organization


Mathematics

Due December 2009

2010. V, 130 p. (Algebra and Applications, Volume 12) Hardcover

7 € 79,95 | £49.957 * € (D) 85,55 | € (A) 87,95 | sFr 124,50ISBN 978-1-84882-940-4

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Mathematics

Due November 2009

2010. X, 460 p. (Springer Monographs in Mathematics) Hardcover


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